Rewrite the equation by completing the square. $x^{2} +7 x +12 = 0$ $(x + $
Solution: $\begin{aligned} x^2 +7 x +12&=0 \\\\ x^2 +7 x&=-12 \end{aligned}$ Now we want to complete $x^2 +7 x$ into a perfect square. To do that, we should add $\left(\dfrac{{7}}{2}\right)^2={\dfrac{49}{4}}$ to it: $x^2{+7}x + {\dfrac{49}{4}}=\left(x +\dfrac{7}{2} \right)^2$ $\begin{aligned} x^2 +7 x&=-12 \\\\ x^2 +7 x + {\dfrac{49}{4}}&=-12 + {\dfrac{49}{4}} \\\\ \left(x +\dfrac{7}{2} \right)^2&=\dfrac{1}{4} \end{aligned}$ In conclusion, the equation after completing the square is written as: $\left(x +\dfrac{7}{2} \right)^2=\dfrac{1}{4}$